Selection with two alleles and complete dominance

For a plant selection model with frequency-independent viabilities, fertilities and selfing rates, it is shown that apart from global fixation, for certain parameter combinations a protected polymorphism and facultative fixation (either allele may become fixed according to initial frequencies) may both occur. Facultative fixation requires different selling rates for the dominant and recessive type. Protection of the polymorphism requires resource allocation for male and female function. In this connection the problem of purely genetically caused population extinction is discussed.
For general frequency dependence and regular segregation, the chances for establishment of a completely recessive gene are compared to those of a completely dominant gene. It is proven that the process of establishment of the recessive gene, despite a fitness advantage, may be considerably endangered by drift effects if random mating prevails. The recessive gene may reach the same effectivity in establishment as a dominant gene, only if the recessive homozygote mates exclusively with its own type during the period of establishment.     

Temporal changes in allele frequencies in two reciprocally selected maize populations

The effects of breeding on allele frequency changes at 82 restriction fragment length polymorphism (RFLP) loci were examined in two maize (Zea mays L.) populations undergoing reciprocal recurrent selection, Iowa Stiff Stalk Synthetic and Iowa Corn Borer Synthetic #1. After 12 cycles of selection, approximately 30% of the alleles were extinct and 10% near fixation in each population. A test of selective neutrality identified several loci in each population whose allele frequency changes cannot be explained by genetic drift; interpopulation mean expected heterozygosity increased for that subset of 28 loci but not for the remaining 54 loci. Mean expected heterozygosity within the two subpopulations decreased 39%, while the between-population component of genetic variation increased from 0.5% to 33.4% of the total. Effective population size is a key parameter for discerning allele frequency changes due to genetic drift versus those resulting from selection and genetic hitchhiking. Empirical estimates of effective population size for each population were within the range predicted by the breeding method. Received: 10 June 1998 / Accepted: 29 April 1999     

Conservation corridors affect the fixation of novel alleles

Corridors are a popular tool for conservation of small populations. However, two purported benefits of corridors, increasing gene flow and providing a means for the recolonization of extinct patches of habitat (population rescue), may have unappreciated impacts on the likelihood that a new allele will become incorporated (fixed) within a population. Using a simulation model, I demonstrate that connecting a stable, isolated population with a population that requires periodic rescue (due to extinction via natural or anthropogenic disturbance) can affect fixation of alleles in the stable population, largely by changing the effective population size Ne of the two-patch complex. When disturbance is rare, connecting the two patches with corridors can increase fixation of beneficial alleles and increase loss of harmful alleles. However, the opposite occurs when rates of disturbance are high: corridors can promote fixation of harmful alleles and reduce fixation of beneficial alleles. Because the impact of corridors hinges upon disturbance frequency (i.e. rate of population rescue), population growth rate, movement rates, and habitat quality, different species are likely to have different responses to corridor-mediated fixation, even if the species reside within the same ecological community. By changing fixation, corridors could thus either promote adaptation or extinction.     

Regular and chaotic cycling in models of ecological genetics

A model of density-dependent selection is investigated for the cyclical behavior associated with the analogous nonlinear models of population growth. If the population size regulating mechanism reacts too sharply to perturbations in population size, regular and chaotic limit cycles may result. It is established analytically that the population may converge to fixation or an invariant polymorphic gene frequency while the population size undergoes regular or chaotic oscillations. The possibility of joint limit cycles in both the population size and gene frequency is demonstrated and investigated numerically. Such cycles may occur even though one or both fixation equilibria are locally stable. In the context of equilibrium cycles it is found that overdominance in carrying capacity is not necessary for the maintenance of genetic variation in the population. Furthermore, the genetic system appears able to exert a stabilizing influence on the overall system.     

Dynamics of mitochondrial polymorphism in a natural population of Drosophila littoralis

During seven years, we observed stable mtDNA polymorphism in a local population of Drosophila littoralis. Using RFLP, a number of mitochondrial haplotypes were revealed, two of which were the core and in condition of stable equilibrium. To explain the absence of fixation of one haplotype, we checked a hypothesis that the D. littoralis population had a complex structure, being subdivided into several partially isolated races existing on the same territory. Analysis of highly hypervariable nuclear sequence of retrotransposons Tv1 showed positive correlation of the mitochondrial haplotype with a particular allelic form of Tv1. This supports the proposal that the D. littoralis natural population forms the population system consisting of genetically differentiated races.     

Fixation in haploid populations exhibiting density dependence II: the quasi-neutral case

We determine fixation probabilities in a model of two competing types with density dependence. The model is defined as a two-dimensional birth-and-death process with density-independent death rates, and birth rates that are a linearly decreasing function of total population density. We treat the 'quasi-neutral case' where both types have the same equilibrium population densities. This condition results in birth rates that are proportional to death rates. This can be viewed as a life history trade-off. The deterministic dynamics possesses a stable manifold of mixtures of the two types. We show that the fixation probability is asymptotically equal to the fixation probability at the point where the deterministic flow intersects this manifold. The deterministic dynamics predicts an increase in the proportion of the type with higher birth rate in growing populations (and a decrease in shrinking populations). Growing (shrinking) populations therefore intersect the manifold at a higher (lower) than initial proportion of this type. On the center manifold, the fixation probability is a quadratic function of initial proportion, with a disadvantage to the type with higher birth rate. This disadvantage arises from the larger fluctuations in population density for this type. These results are asymptotically exact and have relevance for allele fixation, models of species abundance, and epidemiological models.     

Genetic structuring in fluctuating populations

The effect of genetic drift in spatially distributed dispersal-linked and density-regulated populations is studied in a classical one-locus two-allele system. We analyse emergence of genetic differentiation assuming random drift only, where the noise-like variability is due to demographic stochasticity. We find emergence of clusters of sub-units with local allele fixation and persistence of both alleles in lengthy simulations. We demonstrate that local allele fixation (extending over a number of adjoining spatial sub-units) – without global loss of alleles – may occur when the carrying capacities of local patches are small, under a full range population dynamic regimes, when dispersal rate is small, and when redistribution (through dispersal) does not act as global mixer. These results are novel. The key to the observations is that drift is simultaneously influenced by distance-dependent dispersal, demographic stochasticity and autocorrelated population fluctuations due to delayed-density dependence. These are standard elements of contemporary population models in spatially structured context. With stable large populations, no stochasticity and dispersal limited to neighbours only, our model collapses to the stepping-stone model, while with dispersal being random and global, the model collapses to Wright's island model.     

Temporal dynamics and linkage disequilibrium in natural Caenorhabditis elegans populations

Caenorhabditis elegans is a major laboratory model system yet a newcomer to the field of population genetics, and relatively little is known of its biology in the wild. Recent studies of natural populations at a single time point revealed strong spatial population structure and suggested that these populations may be very dynamic. We have therefore studied several natural C. elegans populations over time and genotyped them at polymorphic microsatellite loci. While some populations appear to be genetically stable over the course of observation, others seem to go extinct, with full replacement of multilocus genotypes upon regrowth. The frequency of heterozygotes indicates that outcrossing occurs at a mean frequency of 1.7% and is variable between populations. However, in genetically stable populations, linkage disequilibrium between different chromosomes can be maintained over several years at a level much higher than expected from the heterozygote frequency. C. elegans seems to follow metapopulation dynamics, and the maintenance of linkage disequilibrium despite a low yet significant level of outcrossing suggests that selection may act against the progeny of outcrossings.     

Adaptation,Clonal Interference,and Frequency-Dependent Interactions in a Long-Term Evolution Experiment with Escherichia coli

Twelve replicate populations of Escherichia coli have been evolving in the laboratory for >25 years and 60,000 generations. We analyzed bacteria from whole-population samples frozen every 500 generations through 20,000 generations for one well-studied population, called Ara−1. By tracking 42 known mutations in these samples, we reconstructed the history of this population’s genotypic evolution over this period. The evolutionary dynamics of Ara−1 show strong evidence of selective sweeps as well as clonal interference between competing lineages bearing different beneficial mutations. In some cases, sets of several mutations approached fixation simultaneously, often conveying no information about their order of origination; we present several possible explanations for the existence of these mutational cohorts. Against a backdrop of rapid selective sweeps both earlier and later, two genetically diverged clades coexisted for >6000 generations before one went extinct. In that time, many additional mutations arose in the clade that eventually prevailed. We show that the clades evolved a frequency-dependent interaction, which prevented the immediate competitive exclusion of either clade, but which collapsed as beneficial mutations accumulated in the clade that prevailed. Clonal interference and frequency dependence can occur even in the simplest microbial populations. Furthermore, frequency dependence may generate dynamics that extend the period of coexistence that would otherwise be sustained by clonal interference alone.     

Probability of Fixation and Mean Fixation Time of an Overdominant Mutation

The probability of fixation of an overdominant mutation in a finite population depends on the equilibrium gene frequency in an infinite population (m) and the product (A) of population size and selection intensity. If m < 0.5 (disadvantageous overdominant genes), the probability is generally much lower than that of neutral genes; but if m is close to 0.5 and A is relatively small, it becomes higher. If m > 0.5 (advantageous overdominant genes), the probability is largely determined by the fitness of heterozygotes rather than that of mutant homozygotes. Thus, overdominance enhances the probability of fixation of advantageous mutations. The average number of generations until fixation of an overdominant mutation also depends on m and A. This average time is long when m is close to 0.5 but short when m is close to 0 or 1. This dependence on m and A is similar to that of Robertson's retardation factor.     

Rainfall-driven sex-ratio genes in African buffalo suggested by correlations between Y-chromosomal haplotype frequencies and foetal sex ratio

Background  

The Y-chromosomal diversity in the African buffalo (Syncerus caffer) population of Kruger National Park (KNP) is characterized by rainfall-driven haplotype frequency shifts between year cohorts. Stable Y-chromosomal polymorphism is difficult to reconcile with haplotype frequency variations without assuming frequency-dependent selection or specific interactions in the population dynamics of X- and Y-chromosomal genes, since otherwise the fittest haplotype would inevitably sweep to fixation. Stable Y-chromosomal polymorphism due one of these factors only seems possible when there are Y-chromosomal distorters of an equal sex ratio, which act by negatively affecting X-gametes, or Y-chromosomal suppressors of a female-biased sex ratio. These sex-ratio (SR) genes modify (suppress) gamete transmission in their own favour at a fitness cost, allowing for stable polymorphism.     

Sperm competition and the dynamics of X chromosome drive: stability and extinction

Several empirical studies of sperm competition in populations polymorphic for a driving X chromosome have revealed that Sex-ratio males (those carrying a driving X) are at a disadvantage relative to Standard males. Because the frequency of the driving X chromosome determines the population-level sex ratio and thus alters male and female mating rates, the evolutionary consequences of sperm competition for sex chromosome meiotic drive are subtle. As the SR allele increases in frequency, the ratio of females to males also increases, causing an increase in the male mating rate and a decrease in the female mating rate. While the former change may exacerbate the disadvantage of Sex-ratio males during sperm competition, the latter change decreases the incidence of sperm competition within the population. We analyze a model of the effects of sperm competition on a driving X chromosome and show that these opposing trends in male and female mating rates can result in two coexisting locally stable equilibria, one corresponding to a balanced polymorphism of the SR and ST alleles and the second to fixation of the ST allele. Stochastic fluctuations of either the population sex ratio or the SR frequency can then drive the population away from the balanced polymorphism and into the basin of attraction for the second equilibrium, resulting in fixation of the SR allele and extinction of the population.     

Dynamics of mitochondrial polymorphism in a natural population of <Emphasis Type="Italic">Drosophila littoralis</Emphasis>

During seven years, we observed stable mtDNA polymorphism in a local population of Drosophila littoralis. Using RFLP, a number of mitochondrial haplotypes were revealed, two of which were the core and in condition of stable equilibrium. To explain the absence of fixation of one haplotype, we checked a hypothesis that the D. littoralis population had a complex structure, being subdivided into several partially isolated races existing on the same territory. Analysis of highly hypervariable nuclear sequence of retrotransposons Tv1 showed positive correlation of the mitochondrial haplotype with a particular allelic form of Tv1. This supports the proposal that the D. littoralis natural population forms the population system consisting of genetically differentiated races.     

云南汉族酒精依赖综合征与COMT遗传多态性的关联研究

目的：研究儿茶酚胺氧位甲基转移酶（COMT）的不同基因型及等位基因频率在云南汉族酒精依赖综合征患者组和健康对照组的分布差异。方法：应用聚合酶链式反应．限制性片段长度多态性分析法,对COMT基因的rs2075507、rs737865、rs4680、rsl65599四个基因位点进行特异性扩增,限制性内切酶酶切分型。结果：上述4个候选基因中,COMT基因rs737865位点C／C基因型频率在健康对照组较酒依赖组高,其基因型分布在两组中有差异,且具有统计学意义（P〈0．05）。其余3个位点统计学分析均无显著性差异（P〉0．05）。单倍型分析：上述四个候选基因构建出12种主要单倍型（每种单倍型在对照组和酒依赖组中的频率至少有一个大于1％）,单倍型A—C—A—A有可能是云南汉族酒精依赖发生的一种危险因子（OR：2．865,P=0．003347）。连锁不平衡分析显示：云南汉族人群中,COMT基因的rs2075507和rs737865之间存在着强连锁（D〉0．8）。结论：在云南汉族人群中,COMT基因rs2075507、rs4680和rs165599位点与酒依赖无关联性,rs737865C／C基因型可能是酒精依赖的保护因子,可能降低嗜酒的发生率。单倍型A-C-A-A有可能是云南汉族酒精依赖发生的一种危险因子。云南汉族人群中,COMT基因的rs2075507和rs737865之间存在着强连锁。     

Selective sweeps in multilocus models of quantitative traits

We study the trajectory of an allele that affects a polygenic trait selected toward a phenotypic optimum. Furthermore, conditioning on this trajectory we analyze the effect of the selected mutation on linked neutral variation. We examine the well-characterized two-locus two-allele model but we also provide results for diallelic models with up to eight loci. First, when the optimum phenotype is that of the double heterozygote in a two-locus model, and there is no dominance or epistasis of effects on the trait, the trajectories of selected mutations rarely reach fixation; instead, a polymorphic equilibrium at both loci is approached. Whether a polymorphic equilibrium is reached (rather than fixation at both loci) depends on the intensity of selection and the relative distances to the optimum of the homozygotes at each locus. Furthermore, if both loci have similar effects on the trait, fixation of an allele at a given locus is less likely when it starts at low frequency and the other locus is polymorphic (with alleles at intermediate frequencies). Weaker selection increases the probability of fixation of the studied allele, as the polymorphic equilibrium is less stable in this case. When we do not require the double heterozygote to be at the optimum we find that the polymorphic equilibrium is more difficult to reach, and fixation becomes more likely. Second, increasing the number of loci decreases the probability of fixation, because adaptation to the optimum is possible by various combinations of alleles. Summaries of the genealogy (height, total length, and imbalance) and of sequence polymorphism (number of polymorphisms, frequency spectrum, and haplotype structure) next to a selected locus depend on the frequency that the selected mutation approaches at equilibrium. We conclude that multilocus response to selection may in some cases prevent selective sweeps from being completed, as described in previous studies, but that conditions causing this to happen strongly depend on the genetic architecture of the trait, and that fixation of selected mutations is likely in many instances.     

Can mutation or fixation biases explain the allele frequency distribution of human single nucleotide polymorphisms (SNPs)?

One of the most abiding controversies in evolutionary biology concerns the role of neutral processes in molecular evolution. A main focus of the debate has been the evolution of isochores, the strong and systematic variation of base composition in mammalian genomes. One set of hypotheses argue that regions of similar GC are owing to localised mutational biases coupled with neutral evolution. The alternatives point to either selection or biased gene conversion as mechanisms to preferentially remove A or T bases, favouring G and C instead. Using a novel method, we compare models including such fixation biases to models based on mutation bias alone, under the assumption that non-coding, non-repetitive human DNA is at compositional equilibrium. While failing to fully explain the allele frequency distributions of recent single nucleotide polymorphism data, we show that the data are best fitted if the mutation bias is assumed to be constant across the genome, while fixation bias varies with GC content. We also attempt to estimate the strength of fixation bias, which increases linearly with increasing GC. Our approximation suggests that this force exists within the necessary parameter range: it is not so weak as to be drowned by random drift, but not so strong as to lead to exclusive use of G and C alone. Together these results demonstrate that mutation bias fails to explain the evolution of isochores, and suggest that either selection or biased gene conversion are involved.     

Persistence of selfish genetic elements: population structure and conflict

Selfish genetic elements are vertically transmitted factors that spread by obtaining a transmission advantage relative to the rest of the genome of their host organism, often with a cost to overall host fitness. In many cases, conventional population genetics theory predicts them spreading through populations, reaching fixation and becoming undetectable or sometimes driving the population extinct. However, in several well studied systems, these genetic elements are known to persist at relatively low, stable frequencies. Recent research suggests that several processes might explain these observations, including population structure, intragenomic conflict and coevolution.     

Genetic variation in populations of the endangered fish Ladigesocypris ghigii and its implications for conservation

1. The genetic variation of the endangered freshwater fish Ladigesocypris ghigii, endemic to the island of Rhodes (Greece), was investigated for nine populations, originating from seven different stream systems and a reservoir, both at the mtDNA and nuclear level, in order to suggest conservation actions. 2. Both restriction fragment length polymorphism analysis of five segments of mitochondrial DNA (ND‐5/6, COI and 12S‐16S rRNA) amplified by polymerase chain reaction, and random amplified polymorphic DNA analysis, revealed extremely low levels of intra‐population polymorphism. It is highly likely that the low intra‐population variability is the result of successive bottleneck events evident in shrinkage and expansion of the populations year after year, which may have led to a complete loss of several genotypes and haplotypes, and an increased degree of inbreeding. 3. Inter‐population genetic structuring was high, with fixation of haplotypes within six of the nine populations and fixation of alleles within populations originating from different waterbodies. It is probable that all haplotypes and/or alleles found were initially represented in all populations. However, because of the long time of isolation coupled with successive bottleneck and subsequent genetic drift, common mtDNA haplotypes and alleles among the populations may have become rare or extinct through stochastic lineage loss. 4. Although nucleotide divergence among haplotypes was very shallow, half of the haplotypes recorded (three of six), resulted from nucleotide changes on the 12S–16S rRNA segments, which are the most conserved part of the mitochondrial genome. This fact may indicate that the observed genetic variation did not necessarily result only from the retention of ancestral polymorphism, but may have arisen through mutation and complete lineage sorting over a relatively small number of generations, once the populations had become isolated from one another. 5. Our data suggest that two of the L. ghigii populations may be on independent evolutionary trajectories. Considering that each population appears so far well adapted within each site, all populations should be managed and conserved separately.     

Population biology of tropical African butterflies. Sex ratio and genetic variation in Acraea encedon

In Uganda the butterfly, Acraea encedon (L.), occurs in well-defined populations that are largely genetically and ecologically isolated from each other. During the course of a large-scale capture-recapture programme about 18,000 different individuals were marked and released, and from these and many recaptures aspects of the population structure were investigated. Some populations are composed of almost all females while in other populations the sex ratio is normal. In the predominantly female populations many females remain unmated and produce infertile eggs, laying them on plants that are not foodplants and on each other. In such populations there is intense aggregating behaviour. Males live longer than females and each male may mate with several different females. There is evidence for the existence of a self-regulating mechanism in the predominantly female populations in which population size and male frequency are reciprocally dependent. Acraea encedon exists in a large variety of sympatric colour forms, the frequency of which varies from population to population. Some colour forms survive better than others. The hindwing of Acraea encedon has 20 black spots each of which can be absent in any particular butterfly. The relative frequency of missing spots varies from population to population. The ecological genetics of Acraea encedon is discussed in relation to theories of mimicry and polymorphism.     

Natural Selection and Y-Linked Polymorphism

Several population genetic models allowing natural selection to act on Y-linked polymorphism are examined. The first incorporates pleiotropic effects of a Y-linked locus, such that viability, segregation distortion, fecundity and sexual selection can all be determined by one locus. It is shown that no set of selection parameters can maintain a stable Y-linked polymorphism. Interaction with the X chromosome is allowed in the next model, with viabilities determined by both X- and Y-linked factors. This model allows four fixation equilibria, two equilibria with X polymorphism and a unique point with both X- and Y-linked polymorphism. Stability analysis shows that the complete polymorphism is never stable. When X- and Y-linked loci influence meiotic drive, it is possible to have all fixation equilibria simultaneously unstable, and yet there is no stable interior equilibrium. Only when viability and meiotic drive are jointly affected by both X- and Y-linked genes can a Y-linked polymorphism be maintained. Unusual dynamics, including stable limit cycles, are generated by this model. Numerical simulations show that only a very small portion of the parameter space admits Y polymorphism, a result that is relevant to the interpretation of levels of Y-DNA sequence variation in natural populations.